MOTIOiN" OF A PARTICLE 285
the center of force upon the direction of the velocity; then it is evident from Fig. 128 that
= p.
r
Substituting this value of cos $ in the preceding equation we obtain
/ /
r2 FIG. 128.
or v=^ = ^. (IV)
P P
(4) The angular momentum of the particle with respect to the center remains constant.
This result is obtained at once by multiplying both sides of equation (III) by m, the mass of the particle. Thus
but mr2co = Ice.
Therefore Iu = mh= constant.
219. Equation of the Orbit. — The general equation of the orbit is found by eliminating t between equations (I) and (III). The analytical reasoning which follows does not need further explanation:
dr __ dr dd __ dr * dt ~" de " dt "" w dd
- \ I [by (III)]
dd du